Gestational diabetes (GD) has been linked with an increased risk of developing metabolic disorders and behavioral abnormalities in the offspring. Oxidative stress is strongly associated with neurodegeneration and cognitive disruption. In the offspring brains in a GD experimental rat model, increased oxidative stress in the prenatal and postnatal stages was reported. However, long-term alterations to offspring behavior and oxidative stress, caused by changes in the cerebral cortex and hippocampus, remain unclear. In this study, we evaluated the effect of GD on young and adult male and female rat offspring in metabolic parameters, cognitive behavior, and oxidative stress. GD was induced using streptozotocin in dams. Next, the offspring were evaluated at two and six months of age. Anxiety-like behavior was evaluated using the elevated plus maze and open field maze; spatial learning and short-term memory were evaluated using the Morris water maze and radial maze, respectively. We determined oxidative stress biomarkers (reactive oxygen species (ROS), lipid peroxidation and glutathione status) and antioxidant enzymes (superoxide dismutase and catalase) in the brain of offspring. We observed that male GD offspring showed a reduced level of anxiety at both ages as they spent less time in the closed arms of the elevated plus maze at adult age ((P = 0.019, d = 1.083 ( size effect)) and spent more time in the open area of an open field (P = 0.0412, d = 0.743) when young and adult age (P = 0.018, d = 0.65). Adult female GD offspring showed a reduced level of anxiety (P = 0.036; d = 0.966), and young female GD offspring showed a deficiency in spatial learning (P = 0.0291 vs. control, d = 3.207). Adult male GD offspring showed a deficiency in short-term memory (P = 0.017, d = 1.795). We found an increase in ROS and lipid peroxidation, a disruption in the glutathione status, and decreased activity of catalase and superoxide dismutase (P < 0.05 vs. control, d > 1.0), in the cerebral cortex and hippocampus of male and female GD offspring. GD altered metabolism; male offspring of both ages and adult females showed a high level of triglycerides and a lower level of high-density lipoprotein-cholesterol (P < 0.05 vs. control, d > 1.0). Young and adult female offspring displayed higher insulin levels (P < 0.05, d > 1.0). These results suggest that gestational diabetes modifies oxidative stress and cognitive behavior in an age- and sex-dependent manner.